begin{abstract} The relations between the spectrum of the matrix $Q+R$ and the spectra of the matrices $(gamma + delta)Q+(alpha + beta)R-QR-RQ$, $QR-RQ$, $alpha beta R-QRQ$, $alpha RQR-(QR)^{2}$, and $beta R-QR$ have been given on condition that the matrix $Q+R$ is diagonalizable, where $Q$, $R$ are ${alpha, beta}$-quadratic matrix and ${gamma, delta}$-quadratic matrix, respectively, of ord...

We construct the two-variable p-adic q-L-function which interpolates the generalized q-Bernoulli polynomials associated with primitive Dirichlet character χ. Indeed, this function is the q-extension of two-variable p-adic L-function due to Fox, corresponding to the case q = 1. Finally, we give some p-adic integral representation for this two-variable p-adic q-L-function and derive to q-extensio...

let $g $ be a finite group and let $gamma(g)$ be the prime graph‎ ‎of g‎. ‎assume $2 < q = p^{alpha} < 100$‎. ‎we determine finite groups‎ ‎g such that $gamma(g) = gamma(u_3(q))$ and prove that if $q neq‎ ‎3‎, ‎5‎, ‎9‎, ‎17$‎, ‎then $u_3(q)$ is quasirecognizable by prime graph‎, ‎i.e‎. ‎if $g$ is a finite group with the same prime graph as the‎ ‎finite simple group $u_3(q)$‎, ‎then $g$ has a un...

Let $L(s,\chi)$ be the Dirichlet $L$-function associated to a non trivial primitive character $\chi$ defined $\bmod\ q$, where $q$ is an odd prime. In this paper we introduce fast method compute $\vert L(1,\chi) \vert$ using values of Euler's $\Gamma$ function. We also alternative way computing $\log \Gamma(x)$ and $\psi(x)= \Gamma^\prime/\Gamma(x)$,$x\in(0,1)$. Using such algorithms numericall...

Let $G$ be a finite group. We construct the prime graph of $ G $,which is denoted by $ Gamma(G) $ as follows: the vertex set of thisgraph is the prime divisors of $ |G| $ and two distinct vertices $ p$ and $ q $ are joined by an edge if and only if $ G $ contains anelement of order $ pq $.In this paper, we determine finite groups $ G $ with $ Gamma(G) =Gamma(L_3(q)) $, $2 leq q < 100 $ and prov...

We estimate kinematical higher-twist (up to twist 4) corrections the ${\ensuremath{\gamma}}^{*}({q}_{1})\ensuremath{\gamma}({q}_{2})\ensuremath{\rightarrow}M({p}_{1})\overline{M}({p}_{2})$ amplitudes at large ${Q}^{2}=\ensuremath{-}{q}_{1}^{2}$ and small $s=({q}_{1}+{q}_{2}{)}^{2}$, where $M$ is a scalar or pseudoscalar meson. This process known factorize leading into perturbatively calculable ...

we study harmonic analysis on cocommutative kpc-hyper-groups‎, which is a generalization of djs-hypergroups‎, ‎introduced by kalyuzhnyi‎, ‎podkolzin and chapovsky‎. ‎we prove that there is a relationship between‎ ‎the associated measures $mu$ and $gamma mu$‎, ‎where $mu$ is‎ ‎a radon measure on kpc-hypergroup $q$ and $gamma$ is a character on $q$.

There are several statements equivalent to the famous Riemann hypothesis. In 2011, Solé and Planat stated that hypothesis is true if only inequality \(\zeta(2) \cdot \prod_{q\leq q_{n}} (1+\frac{1}{q}) &gt; e^{\gamma} \log \theta(q_{n})\) holds for all prime numbers \(q_{n}&gt; 3\), where \(\theta(x)\) Chebyshev function, \(\gamma \approx 0.57721\) Euler-Mascheroni constant, \(\zeta(x)\) zeta f...